Annotation:Annotationen:Representation and Deduction/M97ac4493l

Annotation of	Annotationen:Representation_and_Deduction
Annotation Comment	[[AnnotationComment::To conclude, let me try to apply this line of thought to the basic understanding of numbers and how they interact. A child can no doubt learn by heart expressions such as “5 + 8 = 13.” However, in order to understand them, she must be able to re-present the meanings of the involved symbols. As in the syllogism, the parts of such numerical expressions involve assumptions. “5” means that one assumes a plurality of countable items which, if they were counted (i.e. if number words were coordinated with them one-to-one), they would use up the number words from “one” to “five.” The “+,” then, signifies that a second plurality of items which, by itself, would use up the number words from “one” to “eight,” is to be counted with the number words that follow upon “five.”[7] Children may re-present these pluralities and the counting activity in many different ways. The sensory-motor material they use to implement the abstracted patterns is irrelevant. What matters is that they have abstracted these patterns and can re-play them in whatever context they might be needed. For I would claim that only if they have acquired a solid facility in the generation of this kind of representation can they possibly enter into the garden of mathematical delights.]]
Last Modification Date	2019-07-26T16:24:17.581Z
Last Modification User	User:Sarah Oberbichler
Annotation Metadata	^"permissions":^"read":ӶӺ,"update":ӶӺ,"delete":ӶӺ,"admin":ӶӺ°,"user":^"id":6,"name":"Sarah Oberbichler"°,"id":"M97ac4493l","ranges":Ӷ^"start":"/divӶ3Ӻ/divӶ4Ӻ/divӶ1Ӻ/divӶ1Ӻ/divӶ3Ӻ","startOffset":6806,"end":"/divӶ3Ӻ/divӶ4Ӻ/divӶ1Ӻ/divӶ1Ӻ/divӶ3Ӻ","endOffset":8062°Ӻ,"quote":"To conclude, let me try to apply this line of thought to the basic understanding of numbers and how they interact. A child can no doubt learn by heart expressions such as “5 + 8 = 13.” However, in order to understand them, she must be able to re-present the meanings of the involved symbols. As in the syllogism, the parts of such numerical expressions involve assumptions. “5” means that one assumes a plurality of countable items which, if they were counted (i.e. if number words were coordinated with them one-to-one), they would use up the number words from “one” to “five.” The “+,” then, signifies that a second plurality of items which, by itself, would use up the number words from “one” to “eight,” is to be counted with the number words that follow upon “five.”Ӷ7Ӻ Children may re-present these pluralities and the counting activity in many different ways. The sensory-motor material they use to implement the abstracted patterns is irrelevant. What matters is that they have abstracted these patterns and can re-play them in whatever context they might be needed. For I would claim that only if they have acquired a solid facility in the generation of this kind of representation can they possibly enter into the garden of mathematical delights.","highlights":Ӷ^"jQuery3210192007916011918022":^°°Ӻ,"text":"To conclude, let me try to apply this line of thought to the basic understanding of numbers and how they interact. A child can no doubt learn by heart expressions such as “5 + 8 = 13.” However, in order to understand them, she must be able to re-present the meanings of the involved symbols. As in the syllogism, the parts of such numerical expressions involve assumptions. “5” means that one assumes a plurality of countable items which, if they were counted (i.e. if number words were coordinated with them one-to-one), they would use up the number words from “one” to “five.” The “+,” then, signifies that a second plurality of items which, by itself, would use up the number words from “one” to “eight,” is to be counted with the number words that follow upon “five.”Ӷ7Ӻ Children may re-present these pluralities and the counting activity in many different ways. The sensory-motor material they use to implement the abstracted patterns is irrelevant. What matters is that they have abstracted these patterns and can re-play them in whatever context they might be needed. For I would claim that only if they have acquired a solid facility in the generation of this kind of representation can they possibly enter into the garden of mathematical delights.","order":"mw-content-text","category":"Schlussfolgerung3","data_creacio":1564151056929°